Properties

Label 2112.4.a
Level $2112$
Weight $4$
Character orbit 2112.a
Rep. character $\chi_{2112}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $58$
Sturm bound $1536$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2112.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 58 \)
Sturm bound: \(1536\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2112))\).

Total New Old
Modular forms 1176 120 1056
Cusp forms 1128 120 1008
Eisenstein series 48 0 48

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(11\)FrickeDim
\(+\)\(+\)\(+\)$+$\(16\)
\(+\)\(+\)\(-\)$-$\(14\)
\(+\)\(-\)\(+\)$-$\(15\)
\(+\)\(-\)\(-\)$+$\(17\)
\(-\)\(+\)\(+\)$-$\(14\)
\(-\)\(+\)\(-\)$+$\(16\)
\(-\)\(-\)\(+\)$+$\(15\)
\(-\)\(-\)\(-\)$-$\(13\)
Plus space\(+\)\(64\)
Minus space\(-\)\(56\)

Trace form

\( 120 q + 1080 q^{9} + O(q^{10}) \) \( 120 q + 1080 q^{9} + 144 q^{13} - 208 q^{17} - 240 q^{21} + 3176 q^{25} - 1008 q^{37} + 944 q^{41} + 5880 q^{49} - 3984 q^{61} + 3072 q^{65} - 1056 q^{69} + 592 q^{73} + 9720 q^{81} + 480 q^{85} - 176 q^{89} - 3696 q^{93} + 3632 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2112))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11
2112.4.a.a 2112.a 1.a $1$ $124.612$ \(\Q\) None 132.4.a.c \(0\) \(-3\) \(-22\) \(20\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-22q^{5}+20q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.b 2112.a 1.a $1$ $124.612$ \(\Q\) None 1056.4.a.a \(0\) \(-3\) \(-14\) \(34\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-14q^{5}+34q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.c 2112.a 1.a $1$ $124.612$ \(\Q\) None 264.4.a.b \(0\) \(-3\) \(-12\) \(-22\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-12q^{5}-22q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.d 2112.a 1.a $1$ $124.612$ \(\Q\) None 66.4.a.b \(0\) \(-3\) \(-10\) \(-16\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-10q^{5}-2^{4}q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.e 2112.a 1.a $1$ $124.612$ \(\Q\) None 132.4.a.d \(0\) \(-3\) \(-10\) \(8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-10q^{5}+8q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.f 2112.a 1.a $1$ $124.612$ \(\Q\) None 132.4.a.b \(0\) \(-3\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+9q^{9}-11q^{11}+88q^{13}+\cdots\)
2112.4.a.g 2112.a 1.a $1$ $124.612$ \(\Q\) None 66.4.a.a \(0\) \(-3\) \(0\) \(14\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+14q^{7}+9q^{9}-11q^{11}-80q^{13}+\cdots\)
2112.4.a.h 2112.a 1.a $1$ $124.612$ \(\Q\) None 33.4.a.b \(0\) \(-3\) \(4\) \(26\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+4q^{5}+26q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.i 2112.a 1.a $1$ $124.612$ \(\Q\) None 264.4.a.c \(0\) \(-3\) \(6\) \(-14\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+6q^{5}-14q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.j 2112.a 1.a $1$ $124.612$ \(\Q\) None 264.4.a.d \(0\) \(-3\) \(6\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+6q^{5}-8q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.k 2112.a 1.a $1$ $124.612$ \(\Q\) None 132.4.a.a \(0\) \(-3\) \(12\) \(-14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+12q^{5}-14q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.l 2112.a 1.a $1$ $124.612$ \(\Q\) None 33.4.a.a \(0\) \(-3\) \(14\) \(-32\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+14q^{5}-2^{5}q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.m 2112.a 1.a $1$ $124.612$ \(\Q\) None 264.4.a.a \(0\) \(-3\) \(18\) \(28\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+18q^{5}+28q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.n 2112.a 1.a $1$ $124.612$ \(\Q\) None 132.4.a.c \(0\) \(3\) \(-22\) \(-20\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-22q^{5}-20q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.o 2112.a 1.a $1$ $124.612$ \(\Q\) None 1056.4.a.a \(0\) \(3\) \(-14\) \(-34\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-14q^{5}-34q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.p 2112.a 1.a $1$ $124.612$ \(\Q\) None 264.4.a.b \(0\) \(3\) \(-12\) \(22\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-12q^{5}+22q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.q 2112.a 1.a $1$ $124.612$ \(\Q\) None 132.4.a.d \(0\) \(3\) \(-10\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-10q^{5}-8q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.r 2112.a 1.a $1$ $124.612$ \(\Q\) None 66.4.a.b \(0\) \(3\) \(-10\) \(16\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-10q^{5}+2^{4}q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.s 2112.a 1.a $1$ $124.612$ \(\Q\) None 66.4.a.a \(0\) \(3\) \(0\) \(-14\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-14q^{7}+9q^{9}+11q^{11}-80q^{13}+\cdots\)
2112.4.a.t 2112.a 1.a $1$ $124.612$ \(\Q\) None 132.4.a.b \(0\) \(3\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{7}+9q^{9}+11q^{11}+88q^{13}+\cdots\)
2112.4.a.u 2112.a 1.a $1$ $124.612$ \(\Q\) None 33.4.a.b \(0\) \(3\) \(4\) \(-26\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+4q^{5}-26q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.v 2112.a 1.a $1$ $124.612$ \(\Q\) None 264.4.a.d \(0\) \(3\) \(6\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+6q^{5}+8q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.w 2112.a 1.a $1$ $124.612$ \(\Q\) None 264.4.a.c \(0\) \(3\) \(6\) \(14\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+6q^{5}+14q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.x 2112.a 1.a $1$ $124.612$ \(\Q\) None 132.4.a.a \(0\) \(3\) \(12\) \(14\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+12q^{5}+14q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.y 2112.a 1.a $1$ $124.612$ \(\Q\) None 33.4.a.a \(0\) \(3\) \(14\) \(32\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+14q^{5}+2^{5}q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.z 2112.a 1.a $1$ $124.612$ \(\Q\) None 264.4.a.a \(0\) \(3\) \(18\) \(-28\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+18q^{5}-28q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.ba 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{33}) \) None 33.4.a.d \(0\) \(-6\) \(-16\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-8-2\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
2112.4.a.bb 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{97}) \) None 66.4.a.c \(0\) \(-6\) \(-10\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-5-\beta )q^{5}+(-1-3\beta )q^{7}+\cdots\)
2112.4.a.bc 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{73}) \) None 1056.4.a.c \(0\) \(-6\) \(-6\) \(-16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-3-\beta )q^{5}+(-8-2\beta )q^{7}+\cdots\)
2112.4.a.bd 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{137}) \) None 264.4.a.f \(0\) \(-6\) \(6\) \(-16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(3+\beta )q^{5}+(-8-2\beta )q^{7}+\cdots\)
2112.4.a.be 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{17}) \) None 264.4.a.e \(0\) \(-6\) \(6\) \(-10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(3+\beta )q^{5}+(-5-\beta )q^{7}+9q^{9}+\cdots\)
2112.4.a.bf 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{185}) \) None 264.4.a.g \(0\) \(-6\) \(6\) \(22\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(3+\beta )q^{5}+(11-\beta )q^{7}+9q^{9}+\cdots\)
2112.4.a.bg 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{97}) \) None 33.4.a.c \(0\) \(-6\) \(14\) \(-24\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(7-\beta )q^{5}+(-12-2\beta )q^{7}+\cdots\)
2112.4.a.bh 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{33}) \) None 33.4.a.d \(0\) \(6\) \(-16\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-8-2\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
2112.4.a.bi 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{97}) \) None 66.4.a.c \(0\) \(6\) \(-10\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-5-\beta )q^{5}+(1+3\beta )q^{7}+\cdots\)
2112.4.a.bj 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{73}) \) None 1056.4.a.c \(0\) \(6\) \(-6\) \(16\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-3-\beta )q^{5}+(8+2\beta )q^{7}+\cdots\)
2112.4.a.bk 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{185}) \) None 264.4.a.g \(0\) \(6\) \(6\) \(-22\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(3+\beta )q^{5}+(-11+\beta )q^{7}+\cdots\)
2112.4.a.bl 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{17}) \) None 264.4.a.e \(0\) \(6\) \(6\) \(10\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(3+\beta )q^{5}+(5+\beta )q^{7}+9q^{9}+\cdots\)
2112.4.a.bm 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{137}) \) None 264.4.a.f \(0\) \(6\) \(6\) \(16\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(3+\beta )q^{5}+(8+2\beta )q^{7}+9q^{9}+\cdots\)
2112.4.a.bn 2112.a 1.a $2$ $124.612$ \(\Q(\sqrt{97}) \) None 33.4.a.c \(0\) \(6\) \(14\) \(24\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(7-\beta )q^{5}+(12+2\beta )q^{7}+9q^{9}+\cdots\)
2112.4.a.bo 2112.a 1.a $3$ $124.612$ 3.3.142161.1 None 264.4.a.h \(0\) \(-9\) \(-4\) \(12\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-1+\beta _{1})q^{5}+(4-\beta _{2})q^{7}+\cdots\)
2112.4.a.bp 2112.a 1.a $3$ $124.612$ 3.3.123209.1 None 264.4.a.i \(0\) \(-9\) \(-4\) \(28\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-1+\beta _{1})q^{5}+(10+\beta _{1}+\beta _{2})q^{7}+\cdots\)
2112.4.a.bq 2112.a 1.a $3$ $124.612$ 3.3.91253.1 None 1056.4.a.g \(0\) \(-9\) \(-2\) \(-8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-1-\beta _{1})q^{5}+(-3-\beta _{1}+\cdots)q^{7}+\cdots\)
2112.4.a.br 2112.a 1.a $3$ $124.612$ 3.3.3957.1 None 1056.4.a.f \(0\) \(-9\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.bs 2112.a 1.a $3$ $124.612$ 3.3.18201.1 None 1056.4.a.e \(0\) \(-9\) \(4\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(1-\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
2112.4.a.bt 2112.a 1.a $3$ $124.612$ 3.3.123209.1 None 264.4.a.i \(0\) \(9\) \(-4\) \(-28\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-1+\beta _{1})q^{5}+(-10-\beta _{1}+\cdots)q^{7}+\cdots\)
2112.4.a.bu 2112.a 1.a $3$ $124.612$ 3.3.142161.1 None 264.4.a.h \(0\) \(9\) \(-4\) \(-12\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-1+\beta _{1})q^{5}+(-4+\beta _{2})q^{7}+\cdots\)
2112.4.a.bv 2112.a 1.a $3$ $124.612$ 3.3.91253.1 None 1056.4.a.g \(0\) \(9\) \(-2\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-1-\beta _{1})q^{5}+(3+\beta _{1})q^{7}+\cdots\)
2112.4.a.bw 2112.a 1.a $3$ $124.612$ 3.3.3957.1 None 1056.4.a.f \(0\) \(9\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.bx 2112.a 1.a $3$ $124.612$ 3.3.18201.1 None 1056.4.a.e \(0\) \(9\) \(4\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(1-\beta _{2})q^{5}+(1+\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.by 2112.a 1.a $4$ $124.612$ 4.4.7338933.1 None 1056.4.a.l \(0\) \(-12\) \(0\) \(12\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-\beta _{1}q^{5}+(3+\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.bz 2112.a 1.a $4$ $124.612$ 4.4.4336977.1 None 1056.4.a.k \(0\) \(-12\) \(10\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(2-\beta _{1})q^{5}+\beta _{3}q^{7}+9q^{9}+\cdots\)
2112.4.a.ca 2112.a 1.a $4$ $124.612$ 4.4.7338933.1 None 1056.4.a.l \(0\) \(12\) \(0\) \(-12\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-\beta _{1}q^{5}+(-3-\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.cb 2112.a 1.a $4$ $124.612$ 4.4.4336977.1 None 1056.4.a.k \(0\) \(12\) \(10\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(2-\beta _{1})q^{5}-\beta _{3}q^{7}+9q^{9}+\cdots\)
2112.4.a.cc 2112.a 1.a $5$ $124.612$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1056.4.a.p \(0\) \(-15\) \(-6\) \(12\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-1-\beta _{1})q^{5}+(2-\beta _{2})q^{7}+\cdots\)
2112.4.a.cd 2112.a 1.a $5$ $124.612$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1056.4.a.o \(0\) \(-15\) \(10\) \(12\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(2+\beta _{1})q^{5}+(2+\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.ce 2112.a 1.a $5$ $124.612$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1056.4.a.p \(0\) \(15\) \(-6\) \(-12\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-1-\beta _{1})q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
2112.4.a.cf 2112.a 1.a $5$ $124.612$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1056.4.a.o \(0\) \(15\) \(10\) \(-12\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(2+\beta _{1})q^{5}+(-2-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2112))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2112)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1056))\)\(^{\oplus 2}\)